Image Thinning

Aria Rajasa Masna – 1201000164

Charles Gunawan – 1201000237

Rama Pandugita – 1201000865

Suluh Legowo –1201001039

Introduction

What is thinning?

Thinning is a morphological operation that is used to remove selected foreground pixels from binary image. The result of thinning operation is a single pixel thickness of the binary image.

How it works?

Thinning operation is carried out by translating the origin of the structuring element (known as kernel) to each possible pixel position in the image, and at each such position comparing it with the underlying image pixels.

If the foreground and background pixels in the structuring element exactly match the foreground and background pixels in the image, then the image pixel underneath the origin of the structuring elements is set to background. Otherwise it left unchanged.

The choice of the structuring element determines under what situations a foreground pixel will be set to background, and hence it determines the application for thinning operation.

The thinning operator is normally applied repeatedly until it causes no further changes to the image, although in some application may only be applied for limited number of iteration.

Thinning Algorithm

Simple algorithm for thinning1. Consider all pixels on the boundaries of

foreground regions (foreground points that have at least on background neighbor).

2. Delete any such point that has more than one foreground neighbor, as long as doing so does not split the existing region.

3. Iterate until no further change can be made (convergence).

Thinning Example

Consider this simple binary image

Thinning Example (cont’d)

Following structuring elements and all their 900 rotations are structuring elements for skeletonization by morphological thinning.

Fig1.a Fig1.b

Thinning Example (cont’d)

At each iteration, the image is first thinned by kernel in fig1.a, and then by the kernel in fig1.b, and then with their remaining six 900 rotations of the two kernels. The process repeated for each pixel in cyclic fashion until none of the thinning produces any further changes. The picture on the left show the iteration sequences for pixel at (0,0).

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Thinning Result

The following figure shows the result of the thinning operation.

Before And After Thinning (1)

Before And After Thinning (2)

Original Image

Binary Image Thinned Image